Bilevel Image Denoising Using Gaussianity Tests

Jérôme Fehrenbach (1, 2) , Mila Nikolova (3) , Gabriele Steidl (4) , Pierre Weiss (1, 2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 ITAV - Institut des Technologies Avancées en sciences du Vivant
3 CMLA - Centre de Mathématiques et de Leurs Applications
4 University of Kaiserslautern [Kaiserslautern]

We propose a new methodology based on bilevel programming to remove additive white Gaussian noise from images. The lower-level problem consists of a parameterized variational model to denoise images. The parameters are optimized in order to minimize a specific cost function that measures the residual Gaussianity. This model is justified using a statistical analysis. We propose an original numerical method based on the Gauss-Newton algorithm to minimize the outer cost function. We finally perform a few experiments that show the well-foundedness of the approach. We observe a significant improvement compared to standard TV-2 algorithms and show that the method automatically adapts to the signal regularity.

Mots clés: Bilevel programming; image denoising; Gaussianity tests; convex optimization

Domaines: Traitement du signal et de l'image [eess.SP]

Jérôme Fehrenbach, Mila Nikolova, Gabriele Steidl, Pierre Weiss. Bilevel Image Denoising Using Gaussianity Tests. 5th International Conference on Scale-Space and Variational Methods in Computer Vision (SSVM 2015), May 2015, Lège Cap Ferret, France. pp.117-128, ⟨10.1007/978-3-319-18461-6_10⟩. ⟨hal-01494632⟩